A360783 - OEIS

%I #12 Feb 20 2023 12:27:25

%S 1,1,1,1,3,7,13,24,55,133,301,678,1639,4120,10253,25591,65869,173551,

%T 459493,1225379,3325123,9162046,25451181,71296499,202144225,579612934,

%U 1675822453,4885178596,14376297345,42690792651,127757371105,385241085261,1170960103855

%N Expansion of Sum_{k>=0} x^k / (1 - k*x^3)^(k+1).

%F a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^k * binomial(n-2*k,k).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^3)^(k+1)))

%o (PARI) a(n) = sum(k=0, n\3, (n-3*k)^k*binomial(n-2*k, k));

%Y Cf. A000248, A360782.

%Y Cf. A000930.

%K nonn,easy

%O 0,5

%A _Seiichi Manyama_, Feb 20 2023